A Negative Value of the Non-Darcy Flow Coefficient in Pore-Fracture Media under Hydro-Mechanical Coupling

The Forchheimer equation is widely used in studying non-Darcy flow. Non-Darcy flow coefficient beta in the Forchheimer equation is generally thought to be positive, and there are few studies on negative values. In this work, we performed seepage tests on sandstone samples with single, T-shaped, and Y-shaped fractures under different confining pressures, water pressures, and angles to analyze the nonlinear seepage behaviors and the features of Forchheimer's coefficients of water flow in pore-fracture media. At the same time, the flow trajectory of the fluid inside the sample is studied by numerical simulation. The results showed that beta was negative in the seepage test in pore-fracture media. The angle of the single-fracture sandstone sample had a greater influence on the seepage characteristic of the pore-fracture media; angles of the sandstone samples with T-shaped and Y-shaped fractures had a relatively small impact. The relationship between beta and inherent permeability k was following a power function, and the differences in the seepage characteristics between the three fractures were compared. The use of the normalized hydraulic conductivity method is used to evaluate the applicability of Darcy's law. Finally, we explained the primary cause of non-linear seepage behaviors with negative beta in fractured sandstone samples.

Automated summary

In this study, seepage tests and numerical simulations were conducted to investigate the non-linear seepage behaviors and Forchheimer's coefficients in pore-fracture media. The results showed that beta can be negative in the seepage tests, and the angle of the single-fracture sample had a significant influence on the seepage characteristics. The relationship between beta and inherent permeability k followed a power function, and the applicability of Darcy's law was evaluated using the normalized hydraulic conductivity method. The primary cause of non-linear seepage behaviors with negative beta in fractured sandstone samples was also explained.